Abstract : Ensuring the safety of hydraulic embankment structures, including embankment dams, levees and dykes, is a major concern all over the world. Still today, about one to two large dams fail every year in the world and hundreds, probably thousands, of dykes and levees fail every year in the world. Embankment hydraulic structures can be subject to three potential failure modes: instability, internal erosion and external erosion. The physical parameters driving instability are the pore pressures inside the embankment and its foundation. This failure mode covers both general slope sliding and instabilities due to seismic loadings. Statistics show that 6% of the failure of large embankment dams are due to that process. Internal erosion can be initiated in the embankment and-or in its foundation by four several types of processes: crack erosion, contact erosion, regressive erosion and suffusion. Crack erosion and regressive erosion can lead to one of the most sudden and dangerous failure mode: piping. Statistics show that 46% of the failures of large embankment dams are due to that process. External erosion is due to the detachment of the embankment material by the overtopping flow. Erosion of the upstream toe of dykes and levees can also lead to failures. Statistics show that 48% of the failures of large embankment dams are due to these processes of external erosion. Study of real cases of embankment dam failures and researches performed in the last two decades on hydraulic embankments erosion both show that breach parameters such as the breach peak outflow, the final breach length or the breach opening duration can not be correctly predicted only by geometrical parameters of the embankment and the upstream reservoir. Taking into account the behaviour of the embankment and foundation material under the flow stress, that is called the material erodibility, is now considered essential for safety assessments of that type of structures.Different experimental devices, called erodimeters, have been developed for sediment transport or embankment issues. Their use is always based on an assumption of an erosion law, which is the relation between the rate of erosion i.e. quantity of eroded material per time unit per surface unit and parameters characterizing the flow and the soil material.Two erodimeters have been selected for the assessment of the erodibility of hydraulic embankment structures, based on the physical processes they are representing and their practical characteristics. These two erodimeters are the Jet Erosion Test and the Hole Erosion Test. After presenting the physical principles of these two tests and the modelling upon which they are based, their engineering application is illustrated as well as the research needs that remain.